Physics · nuclei · NEET
Use binding energy (BE), not mass number, as the key idea: energy released Q = (BE of all products) − (BE of the original nucleus). Step 1: Find total BE before = A × (Ebn of parent). Step 2: Find total BE after = sum of (nucleons in each fragment × its Ebn). Step 3: Q = after − before. NCERT example: A=240 nucleus, Ebn = 7.6 MeV, splits into two A=120 fragments each with Ebn = 8.5 MeV. Before = 240 × 7.6 = 1824 MeV. After = 240 × 8.5 = 2040 MeV. Q = 2040 − 1824 = 216 MeV. Shortcut: Q = 240 × (8.5 − 7.6) = 216 MeV.
You multiply the TOTAL number of nucleons by the CHANGE in binding energy per nucleon. Nucleons are conserved (240 before = 120 + 120 after), so Q = (total nucleons) × (Ebn_after − Ebn_before) = 240 × (8.5 − 7.6) = 216 MeV. A common mistake is to multiply only 120 by the difference — that is wrong because both fragments (all 240 nucleons) become more tightly bound.
Higher binding energy per nucleon means the nucleons are held MORE tightly and the system has LOWER energy (binding energy is a negative contribution to mass). Moving from a loosely bound state to a tightly bound state releases the difference as kinetic energy of fragments, neutrons, and gamma rays. So both fission (heavy → two medium nuclei) and fusion (two light → one heavier nucleus) release energy only because the products sit higher on the binding-energy-per-nucleon graph.
Use the mass-defect method: Q = Δm × 931.5 MeV, where Δm = (total mass of reactants) − (total mass of products), in atomic mass units u. If Δm is positive, energy is released. Example from NCERT fusion: two protons form a deuteron plus a positron and release 0.42 MeV. If a problem gives you masses in u, first find Δm, then multiply by 931.5 MeV per u. The binding-energy method and the mass-defect method give the same answer.
Individually the very light nuclei (like two deuterons) have LOW binding energy per nucleon, but the product they form is higher on the binding-energy curve. Because the product is more tightly bound than the reactants, the extra binding energy is released. Fusion needs very high temperature first, so the positively charged nuclei can overcome Coulomb repulsion and get close enough for the nuclear force to act — but once they fuse, energy comes out.
Two equal methods. Binding-energy method: Q = (total BE of products) − (total BE of reactants). Mass-defect method: Q = Δm × 931.5 MeV, where Δm is the mass lost, in u. A positive Q means energy is released.
About 200 MeV per fissioning nucleus, according to NCERT. The estimate using a model A=240 nucleus (Ebn 7.6 MeV) splitting into two A=120 fragments (Ebn 8.5 MeV) gives 240 × 0.9 = 216 MeV, which is of the same order.
Yes. One atomic mass unit of mass defect corresponds to 931.5 MeV of energy through E = mc². So to convert a mass defect in u to energy, multiply by 931.5 MeV.
Fusion releases more energy PER NUCLEON than fission, because light nuclei climb a steeper part of the binding-energy curve. However, a single fission event releases much more TOTAL energy (about 200 MeV) than a single fusion event (a few MeV), because a heavy nucleus has many nucleons.
Nuclear reactions involve changes in nuclear binding energy (millions of eV, MeV), while chemical reactions involve only electron binding energies (a few eV). NCERT notes energies in nuclear processes are about a million times larger than in chemical processes.
